The integral of a function f from a to b
is called its quadrature. Quadrature can be approximated by
a weighted sum of the values
of the function on a uniform grid
from a to b .
Use of the weights (1 4 1)%3 on a grid of three
points is equivalent to
integrating the parabola (polynomial of order 2) fitted
to the function at the points.
Use of these weights is referred to as an application
of Simpson’s Rule.

The foregoing phrases
(based on the development in
Calculus [6]) provide
the weights for Simpson’s Rule and for higher-order
polynomial approximations
as illustrated below: